James clerk Maxwell
was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation describing electricity, magnetism and light as different manifestations of the same phenomenon for the first time Born: June 13, 1831, Edinburgh, Scotland, United Kingdom Died: November 5, 1879, Cambridge, England, United Kingdom Nationality: scottish, a westman |
The James Clerk Maxwell Story (video)
In the ascent of Western Civilzation, its discoveries, its inventions, from gas lamps and horse drawn carriages to the exploration of the universe is the story of men, Westmen. Issac Newton once remarked: if I have seen further than others it is because I have stood upon the shoulders of giants.
James Clerk Maxwell is one of the giants of Western Civilization.
Nobel Prize winner Richard Feynman predicted that from the long view, say from 10,000 years in the future there can be little doubt that the most significant event of the 19th century will be judged to be Maxwell’s discovery of the laws of electrodynamics.
James Clark Maxwell
Nationality: Scottish British, a Westman
Born: June 13, 1831, Edinburgh, United Kingdom
Died: November 5, 1879, Cambridge, United Kingdom
He lived only 48 years.
Before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches on Electricity. I was aware that there was supposed to be a difference between Faraday’s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other’s language. I had also the conviction that this discrepancy did not arise from either party being wrong. I was first convinced of this by Sir William Thomson, whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject.
As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and these compared with those of the professed mathematicians.
For instance, Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance; Faraday saw a medium where they saw nothing but distance; Faraday sought to understand the phenomena in real actions going on in the medium, others were satisfied that they had found the power of action at a distance impressed on the electric fluids. Faraday and Maxwell were two men with very different backgrounds. Faraday was English; Maxwell Scottish. Faraday was the son of a blacksmith of limited means; Maxwell’s father had inherited a substantial estate and hardly needed to practice the law in which he had been trained. Faraday had only a basic, grade-school education;
Maxwell had the finest education available. Faraday was one of the most popular scientific lecturers of his day; Maxwell gained a poor reputation in the classroom.
Faraday knew practically no formal mathematics; Maxwell was one of the finest mathematicians of his time. Faraday’s research became dominant for experimentation in electricity and magnetism; Maxwell’s for electromagnetic theory. One experience they had in common: both were committed Christians. The religious traditions to which they belonged and their spiritual commitments influenced and strengthened their science.
Finally, there is Faraday’s extremely influential, and initially unconventional, championing of the significance of fields. Faraday’s theoretical and philosophical intuition, growing over decades of experimentation and culminating in his 1852 paper “On the Physical Character of the Lines of Magnetic Force,” was, in hindsight, perhaps his most enduring legacy. A young James Clerk Maxwell certainly took him seriously, and turned his ideas into what we now call Maxwell’s equations of electromagnetism. Physics today sees the field of force, not material substance, as the most fundamental natural reality.
A major seed was planted by Faraday, who envisioned a mysterious, invisible “electrotonic state” surrounding the magnet—what we would today call a field. He posited that changes in this electrotonic state are what cause electromagnetic phenomena. And Faraday hypothesized that light itself was an electromagnetic wave. But shaping these ideas into a complete theory was beyond his mathematical abilities. That was the state of affairs when Maxwell came on the scene. Maxwell was a master at spotting analogies in different branches of the natural world, and, in 1856, he began by using the steady flow of an imaginary of an incompressible fluid as an analogy for both electric and magnetic lines of force: the speed and direction of fluid flow in any small region of space represented the density and direction of the lines of force there. This way, he showed that all the known formulae for electric and magnetic forces in static conditions could be derived equally well from the conventional action-at-a-distance theories or from Faraday’s lines of force. A stupendous achievement but, at the time, Maxwell couldn’t think of how to deal with changing lines of force. He set it aside for awhile and pursued other investigations.
Even though 40 years separated Maxwell and Faraday, they became good friends. Six years later Maxwell came up with a new model. He filled all space with imaginary tiny spherical cells that could rotate and were inter-spaced with even smaller particles that acted like ball-bearings. By giving the cells a small but finite mass and a degree of elasticity, Maxwell constructed a mechanical analogy for magnetic and electric lines of force, and showed that any change in one induced a change in the other. This extraordinary model yielded not only all the known formulae of electricity and magnetism, it predicted electromagnetic waves that traveled at a speed determined solely by the basic properties of electricity and magnetism. This speed turned out to be within 1.5 per cent of the experimentally measured speed of light. An absolutely astounding result, but the response of fellow-scientists was muted.
Let that sink in. Let that sink in for a minute. Maxwell’s theoretical construct predicted that light was an electromagnetic phenomena. His model calculated the speed of electromagnetic waves to within 1.5% of the experimentally measured value for the speed of light.
And his fellow scientists were non-plused! Why?
Because the settled science of the day was that The goal in any branch of physics, was to identify nature’s true mechanism, and they regarded Maxwell’s model as an ingenious but flawed attempt to do this for electromagnetism and light. Maxwell’s work was revolutionary and Pioneering.
And
Everyone expected that Maxwell’s next step would be to refine the model but, instead, he put the model on one side and set out to build the whole theory from scratch, using only the laws of dynamics. The result, two years later, was the paper ‘A Dynamical Theory of the Electromagnetic Field’. Here, the spinning cells were replaced by an all-pervading medium that had inertia and elasticity but no specified mechanism. In what seemed like a conjuring trick, he used Joseph Louis Lagrange’s method, which treated a dynamic system like a ‘black box’: by specifying the system’s general characteristics it was possible to derive the outputs from the inputs without knowing the detailed mechanism. This way, he produced what he called the equations of the electromagnetic field; there were twenty of them. When he presented the paper to the Royal Society in October 1864, the audience simply didn’t know what to make of it. A theory based on a bizarre model was bad enough, but one based on no model at all was incomprehensible. But Maxwell’s genius lay in the fact that he turned the mathematics into the model.
In his 1864 paper read at the Royal Society in London Maxwell presented 20 equations involving 20 variables. These equations mathematically expressed all that was known about electricity and magnetism at the time.
Maxwell’s equations basically summarized the work of Hans Christian Oersted, Karl Fredrich Gauss, Andre Ampere, and Michael Faraday. But one thing was new and a completely radical. Maxwell introduced the concept of a displacement current to harmonize and complete his theory.
Stepping back a moment, consider that the year this paper was published, 1864, the American Civil War, a brother’s war was raging. 618,222 men died in the American Civil War, 360,222 from the North and 258,000 from the South — by far the greatest toll of any war in American history
Up to the time Maxwell died, in 1879, and for several years afterwards, no one else really understood his theory. It sat like an exhibit in a glass case, admired but out of reach. The man who made it accessible was a self-taught former telegraph operator, Oliver Heaviside. In 1885 he summed up the theory in what we now call the Maxwell’s four equations.
div E = ρ/ε div H = 0 curl E = –μ∂H/∂t curl H = ε∂E/∂t + J where E and H are the electric and magnetic field force vectors at any point in space,
ε and μ are the fundamental constants of electricity and magnetism, respectively, ρ is the charge density and J is the current density vector.
The first two equations are compact expressions of the inverse-square law for electricity and magnetism. The third and fourth define the relationship between electricity and magnetism, and imply the existence of electromagnetic waves that travel with speed as determined by the electric and magnetic field constants of the medium. 1/√(με). Heaviside had greatly simplified Maxwell’s equations by using his new system of vector analysis, in which three-dimensional vectors were represented by single letters, and by pushing the electric and magnetic potentials to the background, basically ignoring them.
Several points need to be added to complete the story.
First, Maxwell could easily have condensed the theory himself but thought it best to keep options open. Many years later his wisdom was borne out: when Richard Feynman and others used Maxwell’s theory in the development of quantum electrodynamics, they used as primary quantities the very potentials that Heaviside had discarded.
Second, it was Maxwell himself who coined the terms divergence and curl for the now-familiar vector operators. Third, Maxwell did actually use a form of vector representation in his A Treatise on Electricity and Magnetism, published in 1873, but presented it as a kind of optional extra. His vectors there were derived from William Rowan Hamilton’s fearsomely complicated quaternions, which most people, including mathematicians, wanted nothing to do with.
Vector notation only caught on when Heaviside came along with his much simpler system. Finally, consider this: although Maxwell never pursued the point, his equations imply that the speed of light is constant 1/√(με) regardless of the relative velocity of observer and source. This fact necessarily leads to Einstein’s special theory of relativity, which gives us E=mc². Einstein had the portraits of Maxwell and Faraday in his office and said of them:“It would of course be a great step forward if we succeeded in combining the gravitational field and the electromagnetic field into a single structure. Only then could the era in theoretical physics inaugurated by faraday and james clerk maxwell be brought to a satisfactory close. “To help visualize what Maxwell had discovered consider two charges at rest along with their electric lines of force. A dipole if you will. Now imagine them oscillating up and down.
Next on the scene a German, Heinrich Hertz.
In the ascent of Western Civilzation, its discoveries, its inventions, from gas lamps and horse drawn carriages to the exploration of the universe is the story of men, Westmen. Issac Newton once remarked: if I have seen further than others it is because I have stood upon the shoulders of giants.
James Clerk Maxwell is one of the giants of Western Civilization.
Nobel Prize winner Richard Feynman predicted that from the long view, say from 10,000 years in the future there can be little doubt that the most significant event of the 19th century will be judged to be Maxwell’s discovery of the laws of electrodynamics.
James Clark Maxwell
Nationality: Scottish British, a Westman
Born: June 13, 1831, Edinburgh, United Kingdom
Died: November 5, 1879, Cambridge, United Kingdom
He lived only 48 years.
Before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches on Electricity. I was aware that there was supposed to be a difference between Faraday’s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other’s language. I had also the conviction that this discrepancy did not arise from either party being wrong. I was first convinced of this by Sir William Thomson, whose advice and assistance, as well as to his published papers, I owe most of what I have learned on the subject.
As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and these compared with those of the professed mathematicians.
For instance, Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance; Faraday saw a medium where they saw nothing but distance; Faraday sought to understand the phenomena in real actions going on in the medium, others were satisfied that they had found the power of action at a distance impressed on the electric fluids. Faraday and Maxwell were two men with very different backgrounds. Faraday was English; Maxwell Scottish. Faraday was the son of a blacksmith of limited means; Maxwell’s father had inherited a substantial estate and hardly needed to practice the law in which he had been trained. Faraday had only a basic, grade-school education;
Maxwell had the finest education available. Faraday was one of the most popular scientific lecturers of his day; Maxwell gained a poor reputation in the classroom.
Faraday knew practically no formal mathematics; Maxwell was one of the finest mathematicians of his time. Faraday’s research became dominant for experimentation in electricity and magnetism; Maxwell’s for electromagnetic theory. One experience they had in common: both were committed Christians. The religious traditions to which they belonged and their spiritual commitments influenced and strengthened their science.
Finally, there is Faraday’s extremely influential, and initially unconventional, championing of the significance of fields. Faraday’s theoretical and philosophical intuition, growing over decades of experimentation and culminating in his 1852 paper “On the Physical Character of the Lines of Magnetic Force,” was, in hindsight, perhaps his most enduring legacy. A young James Clerk Maxwell certainly took him seriously, and turned his ideas into what we now call Maxwell’s equations of electromagnetism. Physics today sees the field of force, not material substance, as the most fundamental natural reality.
A major seed was planted by Faraday, who envisioned a mysterious, invisible “electrotonic state” surrounding the magnet—what we would today call a field. He posited that changes in this electrotonic state are what cause electromagnetic phenomena. And Faraday hypothesized that light itself was an electromagnetic wave. But shaping these ideas into a complete theory was beyond his mathematical abilities. That was the state of affairs when Maxwell came on the scene. Maxwell was a master at spotting analogies in different branches of the natural world, and, in 1856, he began by using the steady flow of an imaginary of an incompressible fluid as an analogy for both electric and magnetic lines of force: the speed and direction of fluid flow in any small region of space represented the density and direction of the lines of force there. This way, he showed that all the known formulae for electric and magnetic forces in static conditions could be derived equally well from the conventional action-at-a-distance theories or from Faraday’s lines of force. A stupendous achievement but, at the time, Maxwell couldn’t think of how to deal with changing lines of force. He set it aside for awhile and pursued other investigations.
Even though 40 years separated Maxwell and Faraday, they became good friends. Six years later Maxwell came up with a new model. He filled all space with imaginary tiny spherical cells that could rotate and were inter-spaced with even smaller particles that acted like ball-bearings. By giving the cells a small but finite mass and a degree of elasticity, Maxwell constructed a mechanical analogy for magnetic and electric lines of force, and showed that any change in one induced a change in the other. This extraordinary model yielded not only all the known formulae of electricity and magnetism, it predicted electromagnetic waves that traveled at a speed determined solely by the basic properties of electricity and magnetism. This speed turned out to be within 1.5 per cent of the experimentally measured speed of light. An absolutely astounding result, but the response of fellow-scientists was muted.
Let that sink in. Let that sink in for a minute. Maxwell’s theoretical construct predicted that light was an electromagnetic phenomena. His model calculated the speed of electromagnetic waves to within 1.5% of the experimentally measured value for the speed of light.
And his fellow scientists were non-plused! Why?
Because the settled science of the day was that The goal in any branch of physics, was to identify nature’s true mechanism, and they regarded Maxwell’s model as an ingenious but flawed attempt to do this for electromagnetism and light. Maxwell’s work was revolutionary and Pioneering.
And
Everyone expected that Maxwell’s next step would be to refine the model but, instead, he put the model on one side and set out to build the whole theory from scratch, using only the laws of dynamics. The result, two years later, was the paper ‘A Dynamical Theory of the Electromagnetic Field’. Here, the spinning cells were replaced by an all-pervading medium that had inertia and elasticity but no specified mechanism. In what seemed like a conjuring trick, he used Joseph Louis Lagrange’s method, which treated a dynamic system like a ‘black box’: by specifying the system’s general characteristics it was possible to derive the outputs from the inputs without knowing the detailed mechanism. This way, he produced what he called the equations of the electromagnetic field; there were twenty of them. When he presented the paper to the Royal Society in October 1864, the audience simply didn’t know what to make of it. A theory based on a bizarre model was bad enough, but one based on no model at all was incomprehensible. But Maxwell’s genius lay in the fact that he turned the mathematics into the model.
In his 1864 paper read at the Royal Society in London Maxwell presented 20 equations involving 20 variables. These equations mathematically expressed all that was known about electricity and magnetism at the time.
Maxwell’s equations basically summarized the work of Hans Christian Oersted, Karl Fredrich Gauss, Andre Ampere, and Michael Faraday. But one thing was new and a completely radical. Maxwell introduced the concept of a displacement current to harmonize and complete his theory.
Stepping back a moment, consider that the year this paper was published, 1864, the American Civil War, a brother’s war was raging. 618,222 men died in the American Civil War, 360,222 from the North and 258,000 from the South — by far the greatest toll of any war in American history
Up to the time Maxwell died, in 1879, and for several years afterwards, no one else really understood his theory. It sat like an exhibit in a glass case, admired but out of reach. The man who made it accessible was a self-taught former telegraph operator, Oliver Heaviside. In 1885 he summed up the theory in what we now call the Maxwell’s four equations.
div E = ρ/ε div H = 0 curl E = –μ∂H/∂t curl H = ε∂E/∂t + J where E and H are the electric and magnetic field force vectors at any point in space,
ε and μ are the fundamental constants of electricity and magnetism, respectively, ρ is the charge density and J is the current density vector.
The first two equations are compact expressions of the inverse-square law for electricity and magnetism. The third and fourth define the relationship between electricity and magnetism, and imply the existence of electromagnetic waves that travel with speed as determined by the electric and magnetic field constants of the medium. 1/√(με). Heaviside had greatly simplified Maxwell’s equations by using his new system of vector analysis, in which three-dimensional vectors were represented by single letters, and by pushing the electric and magnetic potentials to the background, basically ignoring them.
Several points need to be added to complete the story.
First, Maxwell could easily have condensed the theory himself but thought it best to keep options open. Many years later his wisdom was borne out: when Richard Feynman and others used Maxwell’s theory in the development of quantum electrodynamics, they used as primary quantities the very potentials that Heaviside had discarded.
Second, it was Maxwell himself who coined the terms divergence and curl for the now-familiar vector operators. Third, Maxwell did actually use a form of vector representation in his A Treatise on Electricity and Magnetism, published in 1873, but presented it as a kind of optional extra. His vectors there were derived from William Rowan Hamilton’s fearsomely complicated quaternions, which most people, including mathematicians, wanted nothing to do with.
Vector notation only caught on when Heaviside came along with his much simpler system. Finally, consider this: although Maxwell never pursued the point, his equations imply that the speed of light is constant 1/√(με) regardless of the relative velocity of observer and source. This fact necessarily leads to Einstein’s special theory of relativity, which gives us E=mc². Einstein had the portraits of Maxwell and Faraday in his office and said of them:“It would of course be a great step forward if we succeeded in combining the gravitational field and the electromagnetic field into a single structure. Only then could the era in theoretical physics inaugurated by faraday and james clerk maxwell be brought to a satisfactory close. “To help visualize what Maxwell had discovered consider two charges at rest along with their electric lines of force. A dipole if you will. Now imagine them oscillating up and down.
Next on the scene a German, Heinrich Hertz.